"However, the filing of an SAR does not require the bank to cease doing business with the client in question." This feels broken. Was this intended to prevent competitors from falsely filing SARs against each other to freeze their business? What are the penalties for abusing this system?
"Hey, this persons makes mostly foreign transactions with vague companies" is a SAR. That's not a crime, and it may not be criminal behavior - it's just an indicator that someone should look closer.
Can you imagine if your bank closed your account and refused to do business with you, without any kind of trial or notification, just because you did something that triggered a fraud measure?
Or to put this another way, how many times have you had to call your credit card provider because they stopped a transaction just because it was suspicious, even when it wasn't?